Non-limit-circle criteria for singular Hamiltonian differential systems
type: Item
instance of: scholarly article
title: Non-limit-circle criteria for singular Hamiltonian differential systems
zbMATH Open document ID: 1084.34024
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-04-28T00:00:00Z
review text: The paper deals with the singular Hamiltonian system \[ Jy^{\prime }(t)=[\lambda P(t)+Q(t)]y(t)\tag{1} \] over the interval \([0,+\infty ),\) where \(\lambda \) is a complex parameter, \(J \) is the symplectic matrix, \(P,Q\) are locally integrable complex-valued Hermitian matrices, with \(P\) nonnegative definite. The main focus of the paper is to present sufficient conditions, depending on \(P\) and \(Q,\) for the semi-degenerate system (1) to be in the non-limit-circle case.
Mathematics Subject Classification ID: 34B20
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 2162025
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: deficiency index
zbMATH Keywords: limit-circle case
author: Jiangang Qi
reviewed by: Abdelkader Boucherif
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.12.041
OpenAlex ID: W2054831313
cites work: Discrete and continuous boundary problems
cites work: Q5336643
cites work: Some remarks on a separation and limit-point criterion of second-order, ordinary differential expressions
cites work: On the Strong Limit-n Classification of Linear Ordinary Differential Expressions of Order 2n
cites work: On the Strong and Weak Limit-Point Classification of Second-Order Differential Expressions†
cites work: A Limit-Point Criterion for Second-Order Differential Expressions with Matrix-Valued Coefficients
cites work: The deficiency index problem for powers of ordinary differential expressions
cites work: 1.—On Square-integrable Solutions of Symmetric Systems of Differential Equations of Arbitrary Order.
cites work: $M(\lambda )$ Theory for Singular Hamiltonian Systems with One Singular Point
cites work: A limit-point criterion for linear hamiltonian systems
cites work: On the Strong Limit-Point Classification of Fourth-Order Differential Expressions with Complex Coefficients
cites work: Q5570370
cites work: ABSOLUTELY CONTINUOUS SPECTRA OF DIRAC SYSTEMS WITH LONG RANGE, SHORT RANGE AND OSCILLATING POTENTIALS
cites work: On the Titchmarsh‐Weyl Coefficients for Singular S‐Hermitian Systems II
cites work: On the deficiency indices and self-adjointness of symmetric Hamiltonian systems
cites work: A Vector-Matrix Formulation for Formally Symmetric Ordinary Differential Equations with Applications to Solutions of Integrable Square
cites work: Nonlinear limit-point type solutions of \(n\)th order differential equations
DOI: 10.1016/J.JMAA.2004.12.041
description: scientific article; zbMATH DE number 2162025